Presets
Playback
Apparatus
Model checks
The science
What is modelled
A conducting disc turns through a local magnetic field. The moving metal sees a changing flux, so currents (eddy currents) circulate; by Lenz's law their force opposes the motion. The currents dissipate energy as heat in the disc.
Equations
- Braking torque
τb = k B2 ω / (1 + ω/ω0)with k = 0.43 N m s T-2, ω0 = 105 rad/s: proportional to B2ω at low speed, saturating at high speed. - Rotor:
J dω/dt = τdrive - τb - b ω, b = 0.02 N m s. - Heating
m c dT/dt = τb ω - m c h (T - Tamb). - Terminal speed from
(b/ω0) ω2 + (kB2 + b - τ/ω0) ω - τ = 0.
Checks run in the page
- Low-speed coast-down against the exponential exp(-t/τ) with τ = J / (kB2 + b).
- Energy: lost kinetic energy equals the integral of brake plus friction power.
- Terminal speed of the simulation against the quadratic above.
- Heating at fixed power against the closed exponential rise.
Honest simplifications
The torque law is a calibrated engineering approximation with a phenomenological roll-off, not a field solution (no FEM); temperature is one lumped value and material properties do not change with temperature. The disc cannot reverse in this model.
What to try
- Switch the magnet off and on while spinning: the braking is immediate and the disc heats.
- Double B: the low-speed braking grows fourfold.
- With a motor torque, find the speed where the brake torque curve crosses the motor line (graph 2).